Question

AOB is a diameter and ABCD is a cyclic quadrilateral.If ADC =120° .Find BAC​

Answer 1

Required Answer:-

We know that, the angle subtend by the diameter or semi-circle at any point of the circle is 90°.

Then:

In the above circle, AB is a diameter because O is the centre. Then, ∠ACB = 90°.

Now:

Another property of cyclic quadrilaterals says that, the opposite angles add upto 180°. That means,

∠CDB + ∠CBA = 180°

∠BCD + ∠DAB = 180°

Considering the first equation, We have ∠CDB

⇒ 120° + ∠CBA = 180°

⇒ ∠CBA = 60°

We have got two out of three angles in ∆CBA, and the third angle is ∠BAC, which we have to find. By angle sum property of triangles::

⇒ ∠ABC + ∠BCA + ∠BAC = 180°

⇒ 60° + 90° + ∠BAC = 180°

⇒ ∠BAC + 150° = 180°

⇒ ∠BAC = 30°

Therefore:

The required unknown angle ∠BAC is 30°.

Answer 2

Step-by-step explanation:

BAC = 180 - ADC=180-120=60°